Discussed herein is a method for measuring distance and velocity at a plurality of objects using FMCW radar, in which:                measurements are repeated cyclically with at least two different frequency ramps,        in each measurement, the transmitted signal is mixed with the received signal, and the spectrum of the mixed signal is recorded,        in a matching procedure, the peaks that are in the spectra recorded for various ramps and that belong to the same object are allocated to each other, and the distances and velocities of the objects are calculated from the frequencies of the peaks, and        in a tracking procedure, the objects measured at various times are identified with one another on the basis of the consistency of their distance and velocity data.        
In particular, discussed herein is a method of this type which is used in ranging systems or distance-control systems for motor vehicles.
From practice, a distance-control system, a so-called ACC (adaptive cruise control) system for motor vehicles is known which works with an FMCW (frequency modulated continuous wave) radar. The functioning principle is described in Winner: “Adaptive Cruise Control”, Automotive Electronics Handbook, published by Ronald K. Jurgen, 2nd edition, McGraw-Hill Inc., Chapter 30.1 (1999). The radar waves are emitted continuously, and the frequency is modulated in accordance with a ramp function made up of a cyclical sequence of four ramps having different slopes. The ramps form two pairs, each made up of a rising and a falling ramp. The amounts of the slopes are identical within each pair, but differ from pair to pair. By mixing the transmitted signal with the received signal, which is obtained by reflection of the radar waves at a plurality of objects, a low-frequency signal is formed whose frequency corresponds to the difference between the frequency of the transmitted signal and the frequency of the reflected signal. In each individual measurement, the spectrum of the low-frequency signal is recorded during the duration of one frequency ramp with constant slope. In this spectrum, each object is represented by a peak whose frequency f, according to the following equation, is a function of the distance d and the velocity v (relative velocity) of the object:f=|(2*F/c*T)*d+(2*fs/c)*v|  (1)
Meanings of equation terms:                f peak frequency in the low-frequency signal        F frequency deviation (frequency at the end of the ramp−frequency at the beginning of the ramp)        c speed of light        T modulation duration (of the ramp)        fs frequency of the transmitted signal        
The first term in equation (1) is proportional to the signal propagation time, d/c and the ramp slope F/T. The second term corresponds to the Doppler shift of the reflected signal.
If only one reflecting object is present, distance d and relative velocity v of this object may be calculated from peak frequencies f1 and f2, which are obtained by two measurements with different ramp slopes. To that end, the following equation system is solved:f1=α*d+β*v f2=γ*d+β*v  (2)with:α=2*f/c*T for the first ramp,β=2*fs/c γ=2*F/c*T for the second ramp
Given a plurality of objects, however, ambiguities occur, because it is not clear which peak belongs to which object. In the known method, this ambiguity is eliminated by performing two additional measurements using a different ramp slope. Since the distances and relative velocities of the objects change slightly at most within the time in which the four measurements are performed, the allocation between the peaks and the objects must be carried out so that the same distances and relative velocities are obtained for the first two measurements as for the last two measurements. This allocation of the peaks to the objects is called matching.
For practical applications, for example, in an ACC system, it is generally necessary to be able to track the measured distances and relative velocities of the various objects over a longer period of time. Therefore, in a procedure known as tracking, the objects measured in one measuring cycle must be identified with the objects measured in a preceding cycle. This tracking procedure is based on the criterion that the distances and relative velocities for each object, measured at various times, must yield a plausible and, in particular, physically possible movement of the object.
The U.S. Pat. No. 5,600,561 discusses a method in which only the distances are measured with the aid of radar, and the object velocities are calculated from the changes in distance. The distances measured for various objects are allocated to the individual objects in such a way that the newly recorded distance data are consistent with the previously calculated velocities.
In contrast, an FMCW radar has the advantage that the relative velocities of the objects can be measured directly. However, it is only possible to differentiate various objects from each other both with respect to their distances and with respect to their relative velocities with a limited resolution.